It is the practised state of the art to make pot shaped parts from a sized piece of sheet metal by deep drawing; a hollow cylindrical body may, for example, be formed, its peripheral wall having at least one axial peripheral section with high shaping and fitting accuracy. The disadvantage of this method is that tensions and tolerances in the thickness of the metal wall in the rolled material and varying tensile forces produce a hollow body which differs in shape from the tool and is, in particular, not exactly cylindrical; this is because the peripheral wall moves back resiliently after deep drawing. The production of accurately shaped and accurately fitting pot shaped hollow bodies by ironing e.g. from alloyed steel sheets is a failure because of the high deforming forces required, which cause damage to the shaped part or tools. If the hollow body is to have an axial section of high shaping and fitting accuracy at its peripheral wall, and if the now customary processes of plastic deformation are to be carried out, an additional, subsequent operation with or without cutting, such as shearing, turning or folding, is required.